Characterization and recognition of image-sparse graphs partitionable into image independent sets and image cliques Original Research Article

In this work, we focus on the class of image-sparse graphs, which generalizes the well-known class of cographs. We consider the problem of verifying whether a image-sparse graph is a image-graph, that is, a graph that can be partitioned into image independent sets and image cliques. First, we describe in detail the family of forbidden induced subgraphs for a cograph to be a image-graph. Next, we show that the same forbidden structures suffice to characterize image-sparse graphs which are image-graphs. Finally, we describe how to recognize image-image-sparse graphs in linear time by using special auxiliary cographs.